In this Nov. 13, 2000 photo, Michael Dell, Chairman and CEO of Dell, speaks during his keynote address at Comdex, in Las Vegas.

SAN FRANCISCO — A shareholder rebellion against Dell’s proposed $24.4 billion sale to its founder and other investors is gaining more support, fueling a belief that the struggling personal computer maker will have to wrangle a higher price to get the deal done.

Mutual fund firm T. Rowe Price joined the opposition Tuesday. T. Rowe Price and another shareholder, Southeastern Asset Management, believe that founder and CEO Michael Dell and the investment firm Silver Lake are being allowed to seize control and end Dell Inc.’s 25-year history as a publicly held company for too little money.

“We believe the proposed buyout does not reflect the value of Dell, and we do not intend to support the offer as put forward,” T. Rowe Price Chairman Brian Rogers said in a statement.

T. Rowe Price and Southeastern are the two largest independent shareholders and own nearly 13 percent of the company combined. Michael Dell has committed his 14 percent stake toward the deal, but he is the only investor to own more stock than either of the two.

Although Dell remains one of the world’s largest technology companies, with about $57 billion in annual revenue, it has become less attractive to investors as smartphones and tablet computers siphon sales away from PCs. To make matters worse, Dell has been losing market share to its rivals. The company once was the world’s largest PC maker, but now ranks third behind Hewlett-Packard Co. and Lenovo Group.

Michael Dell believes it will be easier to accelerate Dell’s expansion into more lucrative areas such as technology consulting and business software if the company doesn’t have to cater to Wall Street’s fixation on whether profits are rising from one quarter to the next.

The company, which is based in Round Rock, Texas, said it remains convinced that it is selling at a fair price, which represents a 25 percent premium from where the stock stood before word of the buyout negotiations leaked last month. During the talks, Dell’s board said it also considered a wide range of other alternatives. The proposed price of $13.65 is more than 40 percent below Dell’s stock price of roughly $24 six years ago when Dell returned for a second stint as CEO.

Southeastern, which came out against the proposed deal last week, argues that Dell is worth $23.72 per share, or about $42 billion. T. Rowe Price didn’t provide an estimate of what it believes Dell is worth.

In a Tuesday research note, Jefferies analyst Peter Misek predicted the current offer will have to be sweetened to $15 per share, or nearly $27 billion, to placate riled shareholders.

Dell’s stock is now trading above the current offer, a sign that more investors are becoming convinced the bid will be raised. Dells shares gained 12 cents to $13.81 in late afternoon trading Tuesday.

The door remains open for another suitor to emerge. Dell said it will accept other bids until late March.